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AgentGFM: A Graph Foundation Model with Node-Agent Information-Flow Control

Jingbo Cui, Jitao Zhao, Di Jin, Dongxiao He

Year: 2026Venue: arXiv preprintArea: cs.LGType: PreprintEmbeddings: 81

Intelligence

Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 90%

Last extracted: 8/4/2026, 10:44:10 AM

Summary

The paper introduces AgentGFM, a Graph Foundation Model that treats each node as an autonomous agent capable of controlling information flow. Unlike traditional GNNs with fixed propagation schemes, AgentGFM employs a shared end-to-end trainable policy where nodes make decisions on source reception, signal-channel selection, and halting through a predict-act-observe-correct process. This approach allows for adaptive, node-specific propagation that generalizes across diverse graph topologies and domains.

Entities (8)

AgentGFM · model · 98%Information Flow Control · mechanism · 94%Node Agent · component · 93%Graph Foundation Models · concept · 92%Predict-Act-Observe-Correct · process · 91%Gain-Aware Halting · decision · 88%Signal-Channel Selection · decision · 88%Source Reception · decision · 88%

Relation Signals (6)

AgentGFM → implements → Information Flow Control

confidence 95% · AgentGFM is proposed as a Graph Foundation Model with node-agent information-flow control.

Node Agent → executes → Predict-Act-Observe-Correct

confidence 92% · Each node interacts with the graph through a predict-act-observe-correct process.

Predict-Act-Observe-Correct → includes → Source Reception

confidence 90% · During the act stage, the node makes three decisions: source reception, signal-channel selection and gain-aware node-wise halting.

Predict-Act-Observe-Correct → includes → Signal-Channel Selection

confidence 90% · During the act stage, the node makes three decisions: source reception, signal-channel selection and gain-aware node-wise halting.

Predict-Act-Observe-Correct → includes → Gain-Aware Halting

confidence 90% · During the act stage, the node makes three decisions: source reception, signal-channel selection and gain-aware node-wise halting.

AgentGFM → addresseslimitationof → Graph Foundation Models

confidence 85% · Most existing GFMs rely on manually designed propagation schemes... AgentGFM addresses this limitation by enabling node-agent information-flow control.

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Abstract

Abstract:Graph Foundation Models (GFMs) aim to learn transferable knowledge from multi-domain graphs and adapt to unseen scenarios. As a fundamental source of relational semantics in graphs, the transferability of topological patterns has long been central to GFM research. However, local structural patterns may vary across graphs and even among nodes within the same graph. Despite such structural variation, most existing GFMs rely on manually designed propagation schemes and apply them to new graphs largely unchanged. Such fixed schemes may not suit the diverse structural patterns of different nodes. This raises a key question: can each node autonomously determine how information should be propagated through the graph? We refer to this capability as information-flow control. Inspired by recent advances in agent technology, we formulate this problem as agent-based decision making and treat each node as an agent. Accordingly, we propose AgentGFM, in which all node agents follow a shared end-to-end trainable policy rather than using independent models. For adaptive information-flow control, each node interacts with the graph through a predict-act-observe-correct process. During the act stage, the node makes three decisions: source reception, signal-channel selection and gain-aware node-wise halting. The resulting observation is compared with the prediction and their discrepancy is used to correct the node state and guide subsequent interactions. Extensive experiments across node-level, graph-level and large-scale transfer scenarios demonstrate the effectiveness of AgentGFM across diverse graph topologies.

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AgentGFM: A Graph Foundation Model with Node-Agent Information-Flow Control Jingbo Cui School of Computer Science and Technology, Tianjin UniversityTianjinChina cjb2025244179@tju.edu.cn , Jitao Zhao School of Computer Science and Technology, Tianjin UniversityTianjinChina zjtao@tju.edu.cn , Di Jin School of Computer Science and Technology, Tianjin UniversityTianjinChina jindi@tju.edu.cn and Dongxiao He School of Computer Science and Technology, Tianjin UniversityTianjinChina hedongxiao@tju.edu.cn Abstract. Graph Foundation Models (GFMs) aim to learn transferable knowledge from multi-domain graphs and adapt to unseen scenarios. As a fundamental source of relational semantics in graphs, the transferability of topological patterns has long been central to GFM research. However, local structural patterns may vary across graphs and even among nodes within the same graph. Despite such structural variation, most existing GFMs rely on manually designed propagation schemes and apply them to new graphs largely unchanged. Such fixed schemes may not suit the diverse structural patterns of different nodes. This raises a key question: can each node autonomously determine how information should be propagated through the graph? We refer to this capability as information-flow control. Inspired by recent advances in agent technology, we formulate this problem as agent-based decision making and treat each node as an agent. Accordingly, we propose AgentGFM, in which all node agents follow a shared end-to-end trainable policy rather than using independent models. For adaptive information-flow control, each node interacts with the graph through a predict–act–observe–correct process. During the act stage, the node makes three decisions: source reception, signal-channel selection and gain-aware node-wise halting. The resulting observation is compared with the prediction and their discrepancy is used to correct the node state and guide subsequent interactions. Extensive experiments across node-level, graph-level and large-scale transfer scenarios demonstrate the effectiveness of AgentGFM across diverse graph topologies. Graph Representation Learning, Graph Neural Networks, Graph Foundation Models †copyright: none†conference: ; ; †ccs: Computing methodologies Neural networks†ccs: Information systems Data mining†ccs: Computing methodologies Transfer learning 1. Introduction Graph-structured data are ubiquitous in real-world applications, including social network analysis (Wu et al., 2019), recommendation systems (Palomares et al., 2021), protein interaction modeling (Vlaic et al., 2018) and knowledge graph reasoning (Schlichtkrull et al., 2018). However, current graph learning models often remain task-specific, which limits their generality across domains. Inspired by the success of foundation models in natural language processing and computer vision, recent studies have begun to explore Graph Foundation Models (GFMs). These models aim to learn generalizable graph knowledge from multi-domain graphs, enabling rapid adaptation to new scenarios (Liu et al., 2023a). As a fundamental source of relational semantics in graphs, the transferability of topological patterns has long been central to GFM research. However, this transferability is challenged by the fact that local structural patterns may vary across graphs and even among nodes within the same graph. Existing studies have explored topology-aware designs to improve generalization under such structural diversity. Prompt-based methods use topology-aware prompts or structural encodings to adapt pretrained models to graph-specific contexts (Fang et al., 2023; Liu et al., 2023b; Yang et al., 2025; Yu et al., 2025). Other methods improve transferability through structural routing, topology alignment or adaptive aggregation (Zhao et al., 2025b; Wang et al., 2024). Recent studies further use Riemannian representations or mixture-of-experts architectures to model heterogeneous topologies (Sun et al., 2025; Liu et al., 2025, 2026). Transformer-based GFMs also encode graph structures as tokens or graph sequences for general-purpose modeling (Xia et al., 2024; Zhao et al., 2025a). These efforts have advanced GFMs toward topology-aware generalization. Despite this progress, most existing GFMs rely on manually designed propagation schemes and apply them to new graphs largely unchanged. Such fixed schemes may not adapt to the diverse local structural patterns of different nodes. As illustrated in Figure 1(a), a fixed scheme may stop before useful information is reached or continue to aggregate irrelevant neighboring signals. This mismatch between uniform propagation and node-specific structural patterns limits adaptation under topology shift. This raises a key question: can each node autonomously determine how information should be propagated through the graph? We refer to this capability as information-flow control. However, realizing information-flow control is nontrivial. Propagation decisions must adapt to node-specific structures while remaining transferable across unseen graphs. In addition, expanding the propagation range may capture useful structural dependencies but can also introduce irrelevant signals, making it difficult to determine an appropriate propagation process for each node. The figure contains two side-by-side diagrams. The left diagram illustrates preset graph propagation, where a target node may fail to reach useful distant information or may aggregate misleading neighboring signals. The right diagram illustrates AgentGFM, where a node performs a predict–act–observe–correct interaction and selectively controls information sources, signal channels and halting decisions before updating its state through feedback. Figure 1. Motivation of AgentGFM. Preset propagation may miss useful evidence or absorb noisy signals under topology shifts. AgentGFM instead enables node-level information-flow control through source reception, signal-channel selection, gain-aware node-wise halting and prediction–observation feedback. Prior adaptive propagation studies have shown that graph propagation can be conditioned on graph signals rather than following a uniform routine (Xue et al., 2021; Lai et al., 2020). However, these methods are typically optimized for a specific graph distribution or supervision objective. They are not designed to learn transferable decision mechanisms across graphs. Existing GFMs adapt to target graphs mainly through topology-aware prompts or expert routing, while their propagation schemes remain largely fixed. Thus, how to enable node-specific propagation decisions that transfer across unseen graphs remains underexplored. Inspired by recent advances in agent technology, we connect this problem with agent-based decision making, where agents adapt their actions according to internal states and environmental feedback. This paradigm naturally aligns with graph information-flow control, where each node should determine how information is received and propagated. Motivated by this perspective, we treat each node as an agent that makes propagation decisions according to its current state and refines them through feedback from the graph. Importantly, node agents do not use independent models. Instead, all nodes follow a shared end-to-end trainable policy, enabling node-specific decisions while preserving cross-graph transferability. Accordingly, we propose AgentGFM, a Graph Foundation Model with node-agent information-flow control. As illustrated in Figure 1(b), each node interacts with the graph through a predict–act–observe–correct process. It first predicts the contextual information expected from its current state and then makes three decisions during the act stage: source reception, signal-channel selection and gain-aware node-wise halting. The graph returns an observation induced by these decisions and the discrepancy between the observation and prediction is used to correct the node state and guide subsequent interactions. Through this process, different nodes follow distinct information-flow trajectories under the same transferable policy. Our contributions are summarized as follows: • We identify the limitation of transferring manually designed propagation schemes to new graphs largely unchanged and formulate topology generalization as node-agent information-flow control. • We propose AgentGFM, where each node acts as an agent under a shared trainable policy and controls information flow through a predict–act–observe–correct process with source reception, signal-channel selection and gain-aware halting. • Extensive experiments across node-level, graph-level and large-scale transfer scenarios demonstrate the effectiveness of AgentGFM across diverse graph topologies. 2. Related Work 2.1. Graph Foundation Models Graph Foundation Models (GFMs) aim to learn transferable graph knowledge that generalizes across graphs. Existing GFMs mainly address cross-graph heterogeneity from two perspectives: feature alignment and structural adaptation. For feature heterogeneity, GCOPE (Zhao et al., 2024) introduces coordinator modules for cross-graph interaction and latent-space alignment, MDGPT (Yu et al., 2024) uses domain-specific tokens to incorporate domain information, TIG (Zhao et al., 2026) learns transfer-invariant node features and BRIDGE (Yuan et al., 2025) combines feature unification with semantic alignment. These methods mainly improve transferability by learning compatible feature spaces. For structural heterogeneity, GraphControl (Zhu et al., 2024) constructs structure-aware positional encodings from spectral information, GFT (Wang et al., 2024) learns transferable propagation patterns, R-GFM (Liu et al., 2026) captures geometry-adaptive representations and GraphAny (Zhao et al., 2025b) adopts mixture-of-experts to adapt encoders to different graph structures. Although these methods improve GFMs through feature alignment, structural encoding, or component adaptation, they mainly adapt model representations or components to target graphs. How individual nodes should adjust their information propagation process under diverse structural conditions remains largely unexplored. AgentGFM addresses this limitation by enabling node-agent information-flow control through a shared transferable policy. 2.2. Adaptive Graph Propagation and Decision-based Reasoning Adaptive graph propagation and decision-based reasoning methods learn how information should be acquired over graph structures instead of relying on fixed message-passing rules. Existing studies mainly adapt information sources or propagation depths. DeepPath (Xiong et al., 2017) and MINERVA (Das et al., 2018) formulate knowledge graph reasoning as path navigation, GDPNet (Xue et al., 2021) learns adaptive neighborhood selection and Policy-GNN (Lai et al., 2020) learns node-specific propagation iterations. These studies show that graph reasoning benefits from adapting where to collect information and how far to propagate. However, these methods are mainly optimized for a specific task, graph distribution or supervision objective and are not designed for cross-graph transfer. In contrast, AgentGFM learns a shared information-flow policy from multiple source graphs and transfers it to unseen target graphs. It jointly controls information sources, signal channels and propagation duration while using prediction–observation discrepancy for state correction. A mechanism-level comparison is provided in Appendix A. 3. Preliminaries 3.1. Problem Setup Let =(,ℰ,)G=(V,E,X) denote a graph, where V is the node set, ℰE is the edge set and ∈ℝ||×dX ^|V|× d is the node feature matrix. We denote the adjacency matrix by A and the neighborhood of node v by (v)N(v). Each node v∈v is associated with a feature vector v∈ℝdx_v ^d. We consider a cross-domain GFM setting in which the model is trained on a set of source graphs SG_S and evaluated on a disjoint set of target graphs TG_T, where S∩T=∅G_S _T= . The objective is to learn transferable graph knowledge from SG_S and generalize to unseen graphs in TG_T with limited supervision. 3.2. Information-Flow Control Formulation Let v(k)h_v^(k) denote the representation of node v at propagation step k. Conventional message passing first aggregates neighboring representations: (1) v(k)=AGG(k)⁡(u(k)∣u∈(v)),m_v^(k)=AGG^(k) ( \h_u^(k) u (v) \ ), and then updates the node representation: (2) v(k+1)=ϕ(k)(v(k),v(k)),h_v^(k+1)=φ^(k) (h_v^(k),m_v^(k) ), where AGG(k)AGG^(k) and ϕ(k)φ^(k) are specified by the model architecture. Consequently, the same propagation mechanism is typically applied to different nodes and transferred to new graphs with limited adaptation. To support node-specific propagation, we formulate information-flow control as a policy-learning problem. At step k, node v constructs a state (3) v(k)=fs(v(k),v(k)),s_v^(k)=f_s (h_v^(k),m_v^(k) ), and a shared policy produces a node-specific decision: (4) v(k)=πθ(v(k)).d_v^(k)= _θ (s_v^(k) ). The representation is then updated through a decision-conditioned transition: (5) v(k+1)=ft(v(k),v(k),v(k)).h_v^(k+1)=f_t (h_v^(k),m_v^(k),d_v^(k) ). This formulation allows different nodes to execute different propagation decisions while sharing the same policy parameters. AgentGFM provides a concrete realization of this formulation in Section 4. 4. Method 4.1. Overview of AgentGFM Given graphs from different domains, AgentGFM first aligns their node features into a shared space using truncated SVD. The aligned features are then processed by a shared encoder in which each node acts as an agent for information-flow control, as illustrated in Figure 2. The encoder operates through a recurrent predict–act–observe–correct process. The process is organized into a small number of outer interaction rounds. Across rounds, each node updates its state using the feedback from the preceding prediction–observation comparison, while the act stage performs an inner information-flow rollout over the graph. At each round, a node first predicts the information expected from its current state. It then makes propagation decisions, receives the resulting information from the graph and updates its state according to the discrepancy between the prediction and observation. All nodes follow the same end-to-end trainable policy while making node-specific decisions. The following subsections introduce the node-level actions, observation construction, state correction and training objectives. 4.2. Node-Agent Information-Flow Control AgentGFM realizes information-flow control through interactions between node agents and the graph. Each node acts as an agent, while the graph serves as the environment that returns contextual information in response to the node’s actions. A node agent is not an independent model assigned to a node. Instead, it is a node-specific execution of a shared information-flow policy. All nodes share the same policy parameters, while their states, actions, observations and halting decisions remain node-specific. For node viv_i, we define its agent state at rollout step t as (6) it=it,s_i^t=c_i^t, where it∈ℝdc_i^t ^d is the carrier state, d denotes the hidden representation dimension and i0=ic_i^0=h_i. Given its_i^t, the shared policy produces (7) it=(it,it,zit),d_i^t= ( γ_i^t, ρ_i^t,z_i^t ), where it γ_i^t and it ρ_i^t represent edge-wise source-reception and signal-channel decisions, while zitz_i^t denotes node-wise halting. The node agent repeatedly executes these decisions in the graph environment. At each rollout step, its actions determine how information is received and processed from neighboring nodes. The rollout terminates when zitz_i^t indicates halting or when the maximum rollout length is reached. After the rollout, node viv_i obtains an observation io_i that summarizes the contextual information returned by the graph environment. This observation is compared with the predicted observation ^i o_i and their discrepancy is used to correct the node representation: (8) i′=(i,^i,i),h_i =T (h_i, o_i,o_i ), where (⋅)T(·) denotes the state-correction function and i′h_i is the corrected representation of node viv_i. Overview of AgentGFM. Each node acts as an agent that performs predictive observation, information-flow decisions, graph interaction and feedback-based state correction. Figure 2. Overall architecture of AgentGFM. Multi-domain node attributes are first aligned into a shared feature space. Each node then performs a predict–act–observe–correct interaction, where information-flow actions control source reception, signal-channel selection and halting. The encoder is pretrained with masked reconstruction and prediction-observation alignment objectives and transferred to downstream tasks. 4.3. Predictive Observation Estimation At the beginning of each interaction round, node viv_i predicts the observation expected from the graph environment based on its current state. This prediction provides a reference for evaluating the information returned after the node executes its actions. Given the current state i=is_i=h_i, the predicted observation is computed as (9) ^i=fpred(i), o_i=f_pred (h_i ), where fpred:ℝd→ℝdf_pred:R^d ^d is a trainable prediction function. ^i o_i denotes the observation that node viv_i expects to receive from the graph environment. After the node acts, the graph environment returns an actual observation io_i. AgentGFM compares ^i o_i with io_i to measure their discrepancy. This discrepancy reflects the mismatch between the node’s current expectation and the information returned by the graph. It is used as feedback to correct the node state and guide the propagation decision in the next interaction round. 4.4. Policy-Conditioned Information-Flow Rollout After predictive observation estimation, each node interacts with the graph environment through a policy-conditioned information-flow rollout over the original topology. At rollout step t, node viv_i decides which sources to receive information from and which signal channel to use for message transmission. Let itc_i^t denote the carrier state of node viv_i at step t, with i0=ic_i^0=h_i. Each node maintains a forwarding budget bit∈[0,1]b_i^t∈[0,1] and an activity variable aita_i^t. The forwarding budget controls the information transmitted by the source node, while aita_i^t indicates whether node viv_i remains active during the rollout. The activity variable follows a binary halting trajectory in the forward pass and is optimized through the straight-through estimator introduced in Section 4.5. For each original edge (u,i)∈ℰ(u,i) , AgentGFM computes a source-reception score: (10) γu→it=σ(gγ(ut,it,ϵu,ϵi,but)), _u→ i^t=σ (g_γ (c_u^t,c_i^t, _u, _i,b_u^t ) ), where ϵu _u and ϵi _i denote feedback cues from the preceding prediction–observation interaction. The score γu→it _u→ i^t determines how strongly node viv_i receives information from source node vuv_u under the current rollout state. The effective transmission strength along edge (u,i)(u,i) is defined as (11) μu→it=aitbutγu→it. _u→ i^t=a_i^tb_u^t _u→ i^t. Accordingly, μu→it∈[0,1] _u→ i^t∈[0,1] is a scalar effective transmission strength. Thus, an active target node receives information according to the source-reception decision, while a source node transmits information according to its forwarding budget. To capture complementary structural signals, AgentGFM constructs low- and high-frequency channels. Let γu→it−1 _u→ i^t-1 denote the source-reception score from the preceding rollout step. For t>0t>0, these scores are normalized over the incoming neighbors: (12) αu→it=sg(γu→it−1)∑v∈(i)sg(γv→it−1)+ε, _u→ i^t= sg ( _u→ i^t-1 ) _v (i)sg ( _v→ i^t-1 )+ , where sg(⋅)sg(·) denotes stop-gradient and ε>0 >0 is a small constant for numerical stability. At the first rollout step, the weights are initialized uniformly over neighboring nodes. Using these policy-conditioned weights, the local low- and high-frequency components are computed as (13) i,lowt=∑u∈(i)αu→itut,i,hight=it−i,lowt.c_i,low^t= _u (i) _u→ i^tc_u^t, _i,high^t=c_i^t-c_i,low^t. The low-frequency component summarizes contextual information from the selected sources, while the high-frequency component preserves the deviation of the node state from its local context. For source node vuv_u, AgentGFM constructs two candidate messages: (14) u,lowt=lowu,lowt,u,hight=highu,hight.m_u,low^t=W_lowc_u,low^t, _u,high^t=W_highc_u,high^t. The edge-specific channel gate ρu→it _u→ i^t is computed from source–target compatibility, feedback cues and the source forwarding budget and is mapped into (0,1)(0,1) through a sigmoid function. It combines the low- and high-frequency messages as (15) u→it=ρu→itu,lowt+(1−ρu→it)λhighu,hight,m_u→ i^t= _u→ i^tm_u,low^t+ (1- _u→ i^t ) _highm_u,high^t, where λhigh _high controls the contribution of the high-frequency channel. Finally, the contextual information received by node viv_i at rollout step t is (16) it=∑u∈(i)μu→itu→it∈ℝd.r_i^t= _u (i) _u→ i^tm_u→ i^t ^d. 4.5. Gain-Aware Halting and Observation Construction After receiving the contextual signal itr_i^t, node viv_i constructs a candidate carrier state: (17) ~it+1=Norm2⁡(it+fc([it∥it]))∈ℝd. c_i^t+1=Norm_2 (c_i^t+f_c ( [c_i^t\|r_i^t ] ) ) ^d. To estimate whether the current information-flow step provides useful additional information, we introduce a local gain predictor fgain(⋅)f_gain(·). It measures the discrepancy between the received context and the predicted context before and after state refinement: (18) di,−t d_i,-^t =1d‖it−fgain(it)‖1, = 1d \|r_i^t-f_gain (c_i^t ) \|_1, di,+t d_i,+^t =1d‖it−fgain(~it+1)‖1, = 1d \|r_i^t-f_gain ( c_i^t+1 ) \|_1, git g_i^t =di,−t−di,+t. =d_i,-^t-d_i,+^t. The resulting predictive gain git∈ℝg_i^t is node-specific. A positive gain indicates that the candidate update better captures the received context, while a small or negative gain suggests limited benefit from further information acquisition. Based on the current carrier state, received context, predictive gain, forwarding budget and rollout-step embedding, a halting policy generates the halting score: (19) κit=fhalt(it,it,~it+1,git,bit,t), _i^t=f_halt (c_i^t,r_i^t, c_i^t+1,g_i^t,b_i^t,e_t ), where t∈ℝ4e_t ^4 denotes a learnable embedding of the current rollout step and κit∈(0,1) _i^t∈(0,1) is the scalar halting score. To retain discrete node-wise execution while enabling end-to-end optimization, we apply a straight-through estimator: (20) zi,ht z_i,h^t =(κit≥θ0), =I ( _i^t≥ _0 ), zit z_i^t =zi,ht+κit−sg⁡(κit), =z_i,h^t+ _i^t-sg ( _i^t ), ait+1 a_i^t+1 =ait(1−zit). =a_i^t (1-z_i^t ). The carrier state is updated according to the activity status at the current rollout step: (21) it+1=ait~it+1+(1−ait)it.c_i^t+1=a_i^t c_i^t+1+ (1-a_i^t )c_i^t. The forward pass follows the binary halting decision, while gradients are propagated through the continuous halting score during optimization. An active node incorporates the contextual information received at the current rollout step. Once a node halts, its carrier state remains unchanged in subsequent rollout steps, while the frozen carrier can still provide source information for active nodes. Finally, the observation of node viv_i is constructed by aggregating the contextual information collected throughout its node-specific information-flow rollout: (22) i=ReLU⁡(LN⁡(∑t=0T−1it)).o_i=ReLU (LN ( _t=0^T-1r_i^t ) ). 4.6. Feedback-Gated State Correction After obtaining the actual observation from the graph environment, each node compares it with the observation predicted from its current state. Their discrepancy reflects how far the returned information deviates from the node’s expectation. AgentGFM uses this discrepancy to regulate the contribution of the actual observation during state correction. We define the prediction–observation discrepancy as (23) i=|i−^i|∈ℝd, δ_i= |o_i- o_i | ^d, where ^i o_i is the predicted observation and io_i is the actual observation returned by the graph environment. This discrepancy is used for the current state correction and can also provide feedback for subsequent interactions. Based on i δ_i, AgentGFM computes a correction gate: (24) i=σ(frel(i,^i,i,i))∈(0,1)d,q_i=σ (f_rel(h_i, o_i,o_i, δ_i) )∈(0,1)^d, where iq_i is a feature-wise correction gate that controls the contribution of each dimension of the actual graph observation. The corrected observation is obtained through gated fusion: (25) ~i=i⊙i+(1−i)⊙^i. o_i=q_i _i+ (1-q_i ) o_i. The node state is then updated through a residual correction: (26) i′=LN⁡(i+Dropout⁡(~i)),h _i=LN (h_i+Dropout( o_i) ), where LN(⋅)LN(·) denotes layer normalization. This feedback-gated correction allows the node to balance the actual graph observation with its prediction before updating the state. Unlike directly weighting messages by their transmission strength, the correction gate is conditioned on the discrepancy between predicted and observed information, making the state update explicitly feedback-driven. Table 1. Cross-domain 1-shot node classification accuracy (%). The best result on each dataset is highlighted in bold. Avg. Rank denotes the average ranking across all datasets, where a lower value is better. A comparison of fourteen graph learning methods across ten node classification datasets under the cross-domain 1-shot protocol. Methods are grouped into task-supervised GNNs, self-supervised pretraining methods and graph foundation models. AgentGFM achieves the best average rank and the highest accuracy on nine datasets. Method Cora CiteSeer PubMed Computers Photo Texas Wisconsin Cornell Chameleon Squirrel Avg. Rank Task-Supervised GNNs GCN 35.08±8.9035.08± 8.90 27.96±7.7727.96± 7.77 49.15±8.9349.15± 8.93 26.96±7.9226.96± 7.92 38.63±7.6038.63± 7.60 34.39±15.5334.39± 15.53 26.90±9.8926.90± 9.89 26.96±8.8926.96± 8.89 21.26±2.5721.26± 2.57 20.71±1.5720.71± 1.57 8.658.65 GAT 35.90±10.4035.90± 10.40 28.85±8.7928.85± 8.79 47.55±11.0547.55± 11.05 28.52±14.4828.52± 14.48 34.10±9.6334.10± 9.63 32.85±15.6532.85± 15.65 25.82±10.8925.82± 10.89 26.58±10.5826.58± 10.58 21.02±2.5221.02± 2.52 20.26±0.9420.26± 0.94 9.909.90 FAGCN 36.93±9.0036.93± 9.00 28.05±8.7928.05± 8.79 50.82±8.6450.82± 8.64 12.47±5.9212.47± 5.92 23.33±7.7223.33± 7.72 32.65±15.9032.65± 15.90 27.64±10.1627.64± 10.16 26.96±8.8326.96± 8.83 21.15±2.8921.15± 2.89 20.57±2.4020.57± 2.40 8.858.85 GPRGNN 41.31±10.4541.31± 10.45 30.86±10.1030.86± 10.10 49.17±10.8949.17± 10.89 33.57±15.2233.57± 15.22 55.09±13.8055.09± 13.80 32.75±14.7132.75± 14.71 24.50±8.7124.50± 8.71 25.78±7.2725.78± 7.27 21.10±2.7021.10± 2.70 20.17±0.9220.17± 0.92 8.808.80 Self-Supervised Pretraining DGI 24.47±4.5824.47± 4.58 25.80±4.1125.80± 4.11 40.60±5.4240.60± 5.42 35.36±9.7635.36± 9.76 47.97±7.0247.97± 7.02 18.49±8.8718.49± 8.87 20.33±11.0320.33± 11.03 16.53±8.0616.53± 8.06 21.43±2.2821.43± 2.28 20.44±1.2520.44± 1.25 10.8010.80 GraphCL 29.52±5.2629.52± 5.26 26.68±4.1326.68± 4.13 40.19±7.2940.19± 7.29 37.74±8.2737.74± 8.27 47.85±7.5847.85± 7.58 20.14±12.9720.14± 12.97 28.39±10.3828.39± 10.38 18.38±8.1618.38± 8.16 22.89±3.2622.89± 3.26 21.16±1.8421.16± 1.84 9.209.20 GraphMAE 41.82±6.5741.82± 6.57 38.32±9.0338.32± 9.03 48.68±8.2948.68± 8.29 43.51±9.6843.51± 9.68 60.25±9.0160.25± 9.01 36.16±15.7236.16± 15.72 25.38±8.6225.38± 8.62 22.84±7.3722.84± 7.37 21.35±3.4121.35± 3.41 21.05±3.9921.05± 3.99 6.306.30 Graph Foundation Models SAMGPT 42.02±6.0142.02± 6.01 39.11±6.9239.11± 6.92 46.49±6.9746.49± 6.97 46.48±8.6746.48± 8.67 58.78±8.6258.78± 8.62 27.46±7.7827.46± 7.78 31.01±7.7831.01± 7.78 30.54±7.0730.54± 7.07 29.37±3.7329.37± 3.73 22.60±2.8222.60± 2.82 5.305.30 BRIDGE 44.43±6.2844.43± 6.28 40.05±6.4940.05± 6.49 50.52±7.5350.52± 7.53 39.67±7.7739.67± 7.77 56.44±8.8956.44± 8.89 31.53±7.9631.53± 7.96 34.26±8.2734.26± 8.27 34.33±7.4134.33± 7.41 28.92±4.5928.92± 4.59 22.52±3.5622.52± 3.56 4.404.40 R-GFM 42.97±5.4142.97± 5.41 51.25±12.4151.25± 12.41 48.38±9.2548.38± 9.25 25.44±5.6625.44± 5.66 57.20±7.2257.20± 7.22 32.98±7.0032.98± 7.00 26.98±5.5826.98± 5.58 21.12±6.0421.12± 6.04 21.83±1.9321.83± 1.93 20.29±0.8020.29± 0.80 7.207.20 GCOPE 43.33±10.0943.33± 10.09 36.61±6.6136.61± 6.61 39.45±8.1839.45± 8.18 28.94±7.9828.94± 7.98 40.86±6.2740.86± 6.27 30.01±8.3330.01± 8.33 36.21±12.3836.21± 12.38 32.70±7.4332.70± 7.43 30.32±4.5630.32± 4.56 23.77±3.6223.77± 3.62 6.206.20 GraphAny 39.25±7.1839.25± 7.18 35.77±6.7635.77± 6.76 52.16±8.3352.16± 8.33 49.11±12.0249.11± 12.02 61.51±9.9561.51± 9.95 34.74±17.7534.74± 17.75 41.37±13.6541.37± 13.65 34.59±12.4634.59± 12.46 25.40±4.1225.40± 4.12 20.42±1.6320.42± 1.63 4.304.30 AgentGFM 51.94±7.2851.94± 7.28 44.32±8.2044.32± 8.20 52.96±9.1552.96± 9.15 55.93±9.5255.93± 9.52 67.48±8.6467.48± 8.64 42.21±13.2042.21± 13.20 44.57±12.9544.57± 12.95 39.83±9.4039.83± 9.40 30.54±4.1730.54± 4.17 24.20±3.5024.20± 3.50 1.101.10 4.7. Training Objective and Optimization AgentGFM is pretrained on source graphs using self-supervised objectives. Given a masked node set ℳM, the masked attribute reconstruction objective is (27) ℒmae=1|ℳ|∑vi∈ℳ‖i−fdec(i′)‖1.L_mae= 1|M| _v_i \|x_i-f_dec(h_i ) \|_1. This objective encourages the model to recover masked attributes using contextual information from the graph rather than relying only on visible node features. To train predictive observation estimation, we align the predicted observation with the actual observation returned by the graph environment: (28) ℒpred=1||∑vi∈(1−^i⊤sg⁡(i)‖^i‖2‖i‖2+ε),L_pred= 1|V| _v_i (1- o_i sg(o_i)\| o_i\|_2\|o_i\|_2+ ), where sg⁡(⋅)sg(·) denotes stop-gradient. To prevent excessive information propagation, we regularize source reception, effective transmission strength and rollout length: (29) ℒγ=t,(u,i)∈ℰ[γu→it],ℒμ=t,(u,i)∈ℰ[μu→it],ℒa=t,i[ait+1].L_γ=E_t,(u,i) [ _u→ i^t ], _μ=E_t,(u,i) [ _u→ i^t ], _a=E_t,i [a_i^t+1 ]. These terms discourage uniformly strong source reception, excessive information transmission and unnecessarily long rollouts, respectively. The final training objective is (30) ℒ=λmaeℒmae+λpredℒpred+λγℒγ+λμℒμ+λaℒa.L= _maeL_mae+ _predL_pred+ _γL_γ+ _μL_μ+ _aL_a. Implementation of learnable components. Observation prediction, carrier updating, gain estimation, gain-aware halting and reliability gating are implemented using lightweight two-layer MLPs, while the edge-level source-reception and low-/high-frequency channel gates combine source–target query–key projections with scalar MLPs. The detailed parameterization, normalization operations and parameter-sharing scheme are provided in Appendix B.3. 5. Experiments 5.1. Experimental Setup 5.1.1. Datasets and Tasks We evaluate AgentGFM on the cross-domain 1-shot setting. For node classification, we use ten datasets, including Texas, Wisconsin, Cornell, Chameleon, Squirrel (Pei et al., 2020), Cora, CiteSeer, PubMed (Yang et al., 2016), Computers and Photo (Shchur et al., 2018). These datasets cover diverse domains and topological patterns, including both homophilous and heterophilous graphs. For graph classification, we evaluate on MUTAG, D (Shervashidze et al., 2011), IMDB-BINARY (Yanardag and Vishwanathan, 2015), ENZYMES (Borgwardt et al., 2005) and PROTEINS (Dobson and Doig, 2003). To further examine scalability, we conduct large-scale node classification experiments on Physics (Shchur et al., 2018), Ogbn-Products and Ogbn-Arxiv (Hu et al., 2020). 5.1.2. Evaluation Protocol We adopt a leave-one-dataset-out cross-domain 1-shot protocol. For each target dataset, the model is pretrained only on the remaining source datasets, ensuring that the target graph is unseen during pretraining. For downstream evaluation, we randomly sample one labeled instance per class as the support set and use its representation as the class prototype. Each remaining instance is assigned to the prototype with the highest cosine similarity. We independently sample the support set 100 times and report the mean accuracy and standard deviation. For graph classification, graph representations are obtained by mean pooling node representations and one labeled graph per class is used to construct the prototypes. All methods are evaluated under identical source–target splits and 1-shot settings. 5.1.3. Baselines We compare AgentGFM with three groups of methods. The first group includes task-supervised GNNs, such as GCN (Kipf and Welling, 2017), GAT (Velickovic et al., 2018), FAGCN (Bo et al., 2021) and GPRGNN (Chien et al., 2021). The second group includes self-supervised graph pretraining methods, such as DGI (Velickovic et al., 2019), GraphCL (You et al., 2020) and GraphMAE (Hou et al., 2022). The third group consists of GFMs, including SAMGPT (Yu et al., 2025), BRIDGE (Yuan et al., 2025), R-GFM (Liu et al., 2026), GCOPE (Zhao et al., 2024) and GraphAny (Zhao et al., 2025b). All methods are evaluated under the same protocol. 5.2. Performance Analysis 5.2.1. Cross-Domain 1-Shot Node Classification Table 1 reports the cross-domain 1-shot node classification results. AgentGFM achieves the best average rank of 1.10 across ten target datasets. It obtains the best performance on nine datasets and remains competitive on CiteSeer. The improvement is especially clear on heterophilous graphs, where fixed propagation rules are more likely to absorb misleading neighboring signals. Baselines exhibit unstable rankings across target datasets, especially under heterophilous settings. In contrast, AgentGFM remains consistently competitive across both homophilous and heterophilous graphs, demonstrating the robustness of topology-adaptive node-agent information-flow control under diverse structural patterns. Table 2. Cross-domain 1-shot graph classification accuracy (%). Method MUTAG IMDB-B ENZYMES PROTEINS D Avg. Rank DGI 58.26±17.7058.26±17.70 51.24±5.8851.24±5.88 18.96±3.1718.96±3.17 54.90±9.8054.90±9.80 53.67±6.2753.67±6.27 5.605.60 GraphCL 56.65±15.8556.65±15.85 51.64±6.1151.64±6.11 19.13±3.0919.13±3.09 55.93±8.3955.93±8.39 54.85±8.3754.85±8.37 4.604.60 GraphMAE 56.72±13.8656.72±13.86 50.78±4.8150.78±4.81 18.66±2.6918.66±2.69 54.77±9.6454.77±9.64 53.41±6.5053.41±6.50 7.607.60 SAMGPT 57.17±13.9157.17±13.91 50.80±3.5550.80±3.55 18.90±4.0018.90±4.00 55.38±10.8755.38±10.87 56.24±7.0056.24±7.00 5.205.20 BRIDGE 55.88±14.2555.88±14.25 52.37±5.8852.37±5.88 20.77±3.7020.77±3.70 55.55±10.7155.55±10.71 56.02±8.9356.02±8.93 3.803.80 R-GFM 58.30±15.0058.30±15.00 51.15±4.4051.15±4.40 20.44±3.1920.44±3.19 55.89±11.2555.89±11.25 55.93±10.9855.93±10.98 3.603.60 GCOPE 57.95±12.6057.95±12.60 51.57±10.0851.57±10.08 19.80±3.4419.80±3.44 55.25±10.2955.25±10.29 55.27±8.7955.27±8.79 4.604.60 AgentGFM 59.52±11.9959.52 11.99 52.59±7.3552.59 7.35 21.50±2.6421.50 2.64 56.87±13.0156.87 13.01 56.50±7.1156.50 7.11 1.001.00 Table 3. Cross-domain 1-shot node classification accuracy (%) on large-scale datasets. The best result on each dataset is highlighted in bold. Cross-domain one-shot node classification accuracy comparison across three large-scale node classification datasets. Method Physics Products Arxiv DGI 50.17±13.1650.17±13.16 9.84±2.729.84±2.72 13.07±2.7613.07±2.76 GraphCL 55.03±9.6655.03±9.66 12.54±3.1712.54±3.17 17.30±4.4517.30±4.45 GraphMAE 70.78±13.0070.78±13.00 4.17±1.534.17±1.53 10.32±2.8510.32±2.85 SAMGPT 63.86±8.5563.86±8.55 15.23±3.3415.23±3.34 15.81±3.2615.81±3.26 BRIDGE 69.18±9.7969.18±9.79 16.25±3.7416.25±3.74 16.97±3.9416.97±3.94 R-GFM 54.25±8.7654.25±8.76 OOM OOM GCOPE 58.89±9.3158.89±9.31 10.65±2.4410.65±2.44 12.89±3.4212.89±3.42 GraphAny 74.18±12.9274.18 12.92 10.89±1.8410.89±1.84 17.99±5.0817.99±5.08 AgentGFM 72.36±7.0872.36±7.08 18.21±3.5518.21 3.55 20.94±3.3320.94 3.33 5.2.2. Cross-Domain 1-Shot Graph Classification Table 2 reports the cross-domain 1-shot graph classification results. AgentGFM ranks first on all five datasets and achieves the best average rank of 1.00. Although the margins over the strongest baselines are modest on some datasets, the consistent improvements across molecular, bioinformatics and social graph benchmarks demonstrate that the transferability of AgentGFM extends to graph-level tasks. We also observe that the strongest baseline varies across datasets, whereas AgentGFM maintains consistently strong performance, suggesting that node-agent information-flow control provides stable graph-level transfer. 5.2.3. Cross-Domain 1-Shot Large-Scale Evaluation Table 3 reports the results on large-scale node classification datasets. AgentGFM is pretrained on eight source graphs, including Cora, CiteSeer, PubMed, Computers, Photo, Texas, Wisconsin and Cornell and then transferred to Physics, Ogbn-Products and Ogbn-Arxiv. AgentGFM achieves the best results on Ogbn-Products and Ogbn-Arxiv and remains competitive on Physics. Notably, R-GFM runs out of memory on Ogbn-Products and Ogbn-Arxiv, whereas AgentGFM completes evaluation on both datasets. AgentGFM performs its rollout over the original edge set without explicitly constructing dense higher-order neighborhoods, which helps retain practical scalability on large graphs. These results demonstrate strong cross-domain transfer performance on large graphs. 5.3. Ablation Study Bar chart showing component-wise ablation results of AgentGFM on representative cross-domain node classification datasets. The full model is compared with variants removing source reception, signal-channel selection, feedback, or halting control. Figure 3. Mechanism-aligned ablation study on cross-domain 1-shot node classification. Distribution of node-specific stopping steps under the maximum rollout horizon. The figure shows the proportion of nodes terminating at different propagation steps across multiple datasets. Figure 4. Distribution of node-specific halting steps in AgentGFM. 5.3.1. Mechanism-Aligned Ablation Following the mechanism-level comparison in Table 6, we evaluate four ablations that isolate the key control mechanisms of AgentGFM: w/o Source-Reception Control, w/o Channel Selection, w/o Feedback and w/o Gain-Aware Halting. These variants remove node-specific source reception, signal-channel selection, prediction–observation feedback and adaptive node-wise halting respectively. Figure 3 presents the results on four representative datasets, while the complete results on all ten node classification datasets are reported in Appendix C. As shown in Figure 3, the full model achieves the best performance on all four datasets. Removing Source-Reception Control consistently reduces accuracy, supporting the contribution of node-specific reception. Removing Channel Selection also degrades performance, with clearer effects on Texas and Cornell, indicating the benefit of adapting signal channels across different graph structures. Removing Feedback causes the largest drops on Cora, CiteSeer and Texas, highlighting the role of prediction–observation feedback in state correction. Gain-Aware Halting further improves performance by allowing nodes to use different rollout lengths. These results empirically support the mechanism-level distinctions summarized in Table 6. Table 4. Hyperparameter analysis of the maximum rollout horizon TmaxT_ . The best result on each dataset is highlighted in bold. Lower average rank indicates better overall performance. Dataset Tmax=2T_ =2 Tmax=3T_ =3 Tmax=4T_ =4 Tmax=5T_ =5 Tmax=6T_ =6 Cora 0.5140 0.5153 0.5154 0.5194 0.5221 CiteSeer 0.4136 0.4291 0.4297 0.4432 0.4343 PubMed 0.5200 0.5182 0.5028 0.5296 0.5101 Computers 0.5504 0.5465 0.5442 0.5593 0.5467 Photo 0.6692 0.6726 0.6627 0.6748 0.6858 Texas 0.4049 0.3924 0.4105 0.4221 0.4153 Wisconsin 0.4339 0.4400 0.4287 0.4457 0.4310 Cornell 0.4001 0.3967 0.4090 0.3983 0.3913 Chameleon 0.2869 0.2891 0.2882 0.3054 0.3027 Squirrel 0.2300 0.2330 0.2341 0.2420 0.2305 Avg. Rank 3.7 3.5 3.6 1.4 2.8 Visualization of the learned information-flow trajectory for target node 1403 from the Cora dataset. The figure shows selected source nodes, propagation hops, edge reception strengths and channel preferences. Figure 5. Node-agent information-flow trace for target node 1403 in Cora. Edge width denotes source-reception strength γ and color indicates channel preference. 5.3.2. Node-Specific Information-Flow Depth Figure 4 shows the distribution of node-specific halting steps under a maximum rollout horizon of T=5T=5. Most nodes halt before reaching the maximum horizon. On average, 82.42% of nodes halt by the second rollout step, showing that AgentGFM does not apply the full rollout to every node. The distributions also vary across datasets. On Cornell, 96.72% of nodes halt by the second step. In contrast, Cora, Computers and Photo retain a larger proportion of nodes at later steps, with 12.52%, 13.69% and 13.13% of nodes halting at steps 4 or 5 respectively. These differences show that AgentGFM does not rely on a single global rollout depth. Instead, different nodes terminate according to their states and estimated propagation gains. Together with the ablation results, this analysis confirms that gain-aware halting actively controls the duration of node-level information acquisition. 5.3.3. Node-Agent Information-Flow Case Study Figure 5 visualizes the learned information-flow trace of target node 1403 in Cora. Each edge represents a source-reception decision, with edge width indicating reception strength and color denoting channel preference. AgentGFM selectively collects information along multiple structural branches, reaching nodes up to five hops away. The varying path lengths, reception strengths and channel preferences show that the shared policy produces a node-specific propagation pattern rather than applying a uniform aggregation rule. 5.3.4. Sensitivity to Rollout Horizon Table 4 reports the sensitivity of AgentGFM to the maximum rollout horizon TmaxT_ . Setting Tmax=5T_ =5 achieves the best average rank and the best performance on seven of ten datasets, showing that a moderate horizon provides sufficient context for most node agents. Smaller horizons may restrict information acquisition, whereas increasing TmaxT_ to 6 brings no consistent improvement and may introduce less useful contextual signals. These results support an adaptive but bounded information-flow rollout and we use Tmax=5T_ =5 as the default setting. 6. Efficiency and Complexity Analysis AgentGFM performs recurrent information-flow rollouts over the original edge set. Let R denote the number of outer predict–act–observe–correct interaction rounds, T the maximum rollout horizon within each round and d the hidden dimension. Source reception, channel selection and message aggregation are computed along existing edges at each rollout step, resulting in a per-step complexity of O(|E|d)O(|E|d) and an overall information-flow complexity of O(RT|E|d)O(RT|E|d). During each rollout step, the node states and edge-level control variables require O(|V|d+|E|)O(|V|d+|E|) memory. Since AgentGFM does not explicitly construct dense higher-order neighborhoods or all-pair structural contexts, it remains scalable for large graphs when R and T are bounded by small constants. Table 5. Efficiency comparison when pretraining on eight source datasets and evaluating on ogbn-arxiv. Method Train Time Train Mem. Test Time Test Mem. BRIDGE 0.72 s 19.62 GB 0.35 s 1.58 GB SAMGPT 0.53 s 8.14 GB 1.24 s 2.35 GB GraphAny 1.75 s 0.67 GB 18.98 s 1.62 GB AgentGFM 1.14 s 10.21 GB 0.89 s 3.24 GB Table 5 reports the empirical efficiency comparison when pretraining on eight source datasets and evaluating on ogbn-arxiv. AgentGFM takes 1.14 seconds per pretraining epoch and 10.21 GB of training memory, which is more memory-efficient than BRIDGE while remaining practical in training time. During target evaluation, AgentGFM takes 0.89 seconds with 3.24 GB of memory, making it faster than GraphAny and SAMGPT at inference. Although AgentGFM is not the fastest or most memory-efficient method in every aspect, it achieves a balanced efficiency profile while retaining adaptive node-agent information-flow control. 7. Conclusion In this paper, we study topology generalization in GFMs through node-agent information-flow control. Existing GFMs typically transfer predefined propagation schemes to new graphs with limited adaptation, which can be restrictive when nodes require different propagation behaviors under unseen topologies. We therefore propose AgentGFM, which treats each node as an agent interacting with the graph environment under a shared transferable policy. Through a predict–act–observe–correct process, AgentGFM enables node-specific source reception, signal-channel selection and gain-aware halting, followed by feedback-gated state correction. 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The comparison focuses on how information-flow execution is determined rather than on specific model architectures. Table 6. Mechanism-level positioning of AgentGFM among graph propagation paradigms. Opt. Signal denotes the objective used for parameter learning, while Interaction Feedback denotes contextual signals used to condition subsequent information-flow decisions. A comparison of six graph propagation paradigms in terms of source control, signal control, depth control, optimization signal and interaction feedback. AgentGFM differs from the other paradigms by combining node- and edge-level source control, low- and high-frequency signal selection, node-wise halting, pretraining objectives and explicit prediction-observation feedback. Paradigm Source Control Signal Control Depth Control Opt. Signal Interaction Feedback Fixed MP Architecture-defined Single Fixed Task loss None Attention MP Attention-weighted Single Fixed Task loss None Multi-hop MP Hop-defined Single Preset Task loss None Adaptive GNNs Learned Limited Adaptive Task loss No explicit feedback Component-Adaptive GFMs Model/expert Model/expert Fixed/expert Pretraining None AgentGFM Node/edge Low/high Node-wise halt Pretraining Pred.–obs. Table 6 distinguishes existing paradigms according to the primary object controlled during information-flow execution. Fixed and multi-hop message passing specify information sources and propagation ranges mainly through the model architecture. Attention-based methods adapt neighbor importance, while adaptive GNNs may further adjust neighborhood selection or propagation depth. However, these methods generally optimize task-specific propagation decisions without explicitly using contextual observations to correct node states and condition subsequent actions. Component-adaptive GFMs mainly adapt prompts, experts, structural encodings, or model components for cross-graph transfer, while the underlying information-flow execution remains largely predetermined. In contrast, AgentGFM treats the node-specific information-flow trajectory as the adaptive object. Each node controls source reception, signal-channel selection and node-wise halting and uses prediction–observation feedback to correct its state and condition subsequent interactions. Appendix B Experimental Settings B.1. Datasets We evaluate node-level performance on a diverse set of benchmark graphs. Citation networks include Cora, CiteSeer and PubMed (Yang et al., 2016). Web page networks consist of Texas, Cornell and Wisconsin (Pei et al., 2020). Wikipedia topic graphs include Chameleon and Squirrel (Pei et al., 2020). E-commerce graphs include Photo and Computers (Shchur et al., 2018). We additionally consider the large-scale ogbn-products and ogbn-arxiv datasets from the Open Graph Benchmark (Hu et al., 2020) and Physics (Shchur et al., 2018) Table 7. Overview of node classification datasets used in the experiments. Statistics of thirteen node classification datasets, including the numbers of nodes, edges, input features and classes. Dataset #Nodes #Edges #Features #Classes Texas 183 325 1,703 5 Cornell 183 298 1,703 5 Wisconsin 251 512 1,703 5 Cora 2,708 10,556 1,433 7 CiteSeer 3,327 9,104 3,703 6 PubMed 19,717 88,648 500 3 Chameleon 2,277 36,101 2,325 5 Squirrel 5,201 217,073 2,089 5 Computers 13,752 491,722 767 10 Photo 7,650 238,162 745 8 Physics 34,493 495,924 8,415 5 ogbn-arxiv 169,343 1,166,243 128 40 ogbn-products 2,449,029 123,718,280 100 47 For graph-level tasks, we use molecular and biological datasets including MUTAG, D (Shervashidze et al., 2011), ENZYMES (Borgwardt et al., 2005) and PROTEINS (Dobson and Doig, 2003). We further include social network datasets IMDB-BINARY (Yanardag and Vishwanathan, 2015). All datasets are commonly used benchmarks in graph representation learning and cover a wide range of graph sizes, structures and homophily characteristics. For graph classification datasets from TUDataset, if the original graphs do not contain node features, we construct node features as follows. If node labels are available, we use one-hot encodings of node labels as node features. Otherwise, we use one-hot encodings of node degrees, where the one-hot dimension is determined by the maximum label value or maximum degree across the entire dataset. If the original dataset provides node features x, we directly use them. Table 8. Overview of graph classification datasets used in the experiments. Avg. Nodes and Avg. Edges denote the average numbers of nodes and edges per graph, respectively. Statistics of five graph classification datasets, including the number of graphs, average graph size, input feature dimension and number of classes. IMDB-BINARY contains no original node attributes. Dataset #Graphs Avg. Nodes Avg. Edges #Features #Classes MUTAG 188 17.9 39.6 7 2 ENZYMES 600 32.6 124.3 3 6 PROTEINS 1,113 39.1 145.6 3 2 IMDB-BINARY 1,000 19.8 193.1 – 2 D 1,178 284.3 1,431.3 89 2 Table 9. Full component ablation results on cross-domain 1-shot node classification. Source-Reception Control corresponds to γ, Channel Selection corresponds to ρ, Feedback denotes prediction–observation feedback and Gain-Aware Halting denotes the node-wise halting mechanism. The best result on each dataset is highlighted in bold. Avg. Rank denotes the average rank across all datasets, where a lower value is better. Method Cora CiteSeer PubMed Computers Photo Texas Wisconsin Cornell Chameleon Squirrel Avg. Rank Full 0.5194 0.4432 0.5296 0.5593 0.6748 0.4221 0.4457 0.3983 0.3054 0.2420 1.2 w/o Source-Reception Control 0.5143 0.4369 0.5238 0.5309 0.6631 0.3949 0.4300 0.3646 0.2930 0.2365 2.9 w/o Channel Selection 0.4962 0.4333 0.4932 0.5152 0.6416 0.3382 0.4063 0.3474 0.2948 0.2342 3.9 w/o Feedback 0.3408 0.3614 0.4220 0.4853 0.3637 0.3211 0.4251 0.3899 0.2990 0.2376 4.2 w/o Gain-Aware Halting 0.5044 0.4195 0.4772 0.5061 0.5857 0.4189 0.4496 0.3720 0.3073 0.2410 2.8 B.2. Implementation Details Table 10. Default hyperparameter settings of AgentGFM. Hyperparameter Value Shared attribute dimension 50 Hidden dimension 128 Interaction rounds R 2 Maximum rollout horizon TmaxT_ 5 Dropout rate 0.10 Masking ratio 0.35 Learning rate 5×10−45× 10^-4 Weight decay 5×10−45× 10^-4 Training epochs 500 Halt threshold θ0 _0 0.55 High-frequency channel coefficient λhigh _high 0.30 λmae _mae 1.00 λpred _pred 0.50 λγ _γ 0.001 λμ _μ 0.001 λa _a 0.001 Number of 1-shot runs 100 We implement AgentGFM in PyTorch and use the same default configuration across all datasets unless otherwise specified. Node attributes are projected into a shared 50-dimensional space and the hidden dimension is set to 128. The model contains two predict–act–observe–correct interaction rounds, with the maximum rollout horizon set to Tmax=5T_ =5. We train AgentGFM for 500 epochs using a learning rate of 5×10−45× 10^-4, a weight decay of 5×10−45× 10^-4, a dropout rate of 0.1 and a masking ratio of 0.35. The complete implementation and hyperparameter settings are summarized in Table 10. For 1-shot evaluation, we repeat the sampling process 100 times and report the mean accuracy and standard deviation. B.3. Information-Flow Policy and Regularization Details This section provides additional details of the node-level information-flow policy and the associated regularizers used in AgentGFM. The policy is shared across nodes and graphs, while its source-reception, channel-selection, forwarding-budget and halting decisions are computed for each local rollout trajectory. B.3.1. Information-Flow Policy Source-reception policy. For each original edge (u,i)∈ℰ(u,i) , the source-reception strength is computed from carrier compatibility, prediction–observation feedback and the source forwarding budget: (31) su→iγ,t=(qγut)⊤(kγit)r+gγ([ϵu‖ϵi‖but]),s_u→ i^γ,t= (W_q^γc_u^t ) (W_k^γc_i^t ) r+g_γ ( [ _u\| _i\|b_u^t ] ), (32) γu→it=σ(su→iγ,t), _u→ i^t=σ (s_u→ i^γ,t ), where ϵu _u and ϵi _i are prediction–observation feedback cues and butb_u^t is the source forwarding budget. The resulting γu→it _u→ i^t measures the source-reception strength from node vuv_u to node viv_i under the current rollout state. Channel-selection policy. The channel-selection gate determines how low- and high-frequency information are combined along each edge. We compute (33) ρu→it=σ(su→iρ,t+βsmoothτρ), _u→ i^t=σ ( s_u→ i^ρ,t+ _smooth _ρ ), where su→iρ,t= s_u→ i^ρ,t= (qρut)⊤(kρit)r (W_q^ρc_u^t ) (W_k^ρc_i^t ) r (34) +gρ([suit‖1−suit‖ϵu‖ϵi‖but]). +g_ρ ( [s_ui^t\|1-s_ui^t\| _u\| _i\|b_u^t ] ). Here, suits_ui^t denotes the cosine-similarity diagnostic between the source and target carrier states. The smoothness bias βsmooth _smooth and temperature τρ _ρ control the preference and sharpness of the low-/high-frequency interpolation. The final message is (35) u→it=ρu→itu,lowt+(1−ρu→it)λhighu,hight.m_u→ i^t= _u→ i^tm_u,low^t+ (1- _u→ i^t ) _highm_u,high^t. A larger ρu→it _u→ i^t assigns greater weight to low-frequency contextual information, whereas a smaller value assigns greater weight to high-frequency residual information. Forwarding-budget update. The forwarding budget represents the current capacity of a node to forward contextual information rather than a monotonically consumed resource. It is updated according to the effective information mass received at the current rollout step: (36) b~it+1=bmin[clip⁡(ηb∑u∈(i)μu→it,0,1)], b_i^t+1=T_b_ [clip ( _b _u (i) _u→ i^t,0,1 ) ], where ηb _b is the budget coefficient and bmin(⋅)T_b_ (·) sets values below bminb_ to zero. The budget state is updated according to the current activity status: (37) bit+1=aitb~it+1+(1−ait)bit.b_i^t+1=a_i^t b_i^t+1+ (1-a_i^t )b_i^t. An active node updates its forwarding budget using the newly received information mass, whereas a halted node retains its previous budget. Stronger received information sustains later propagation, while weak information mass reduces subsequent forwarding capacity. Network parameterization. The observation predictor fpredf_pred, carrier updater fcf_c, gain predictor fgainf_gain, gain-aware halting controller fhaltf_halt and reliability gate frelf_rel are implemented as lightweight two-layer MLPs with PReLU activations and dropout. Layer normalization is applied to representation-valued outputs, whereas sigmoid functions are used for scalar or feature-wise gates. The source-reception and channel-selection policies combine source–target query–key compatibility scores with lightweight scalar MLPs. Within each interaction round, these modules share parameters across all nodes, edges, graph domains and rollout steps, whereas successive interaction rounds use separate parameter sets. B.3.2. Information-Flow Regularization The node-level information-flow policy contains three coupled decisions: which sources to receive from, how much effective information mass to transmit and how long each node should continue its rollout. Without additional constraints, the policy may degenerate into uniformly receiving all neighboring information, transmitting excessive information mass, or keeping most nodes active until the maximum horizon. We therefore regularize these three aspects separately. Source-reception regularization. The first regularizer controls the average source-reception strength: (38) ℒγ=1T|ℰ|∑t=0T−1∑(u,i)∈ℰγu→it.L_γ= 1T|E| _t=0^T-1 _(u,i) _u→ i^t. This term discourages the policy from assigning uniformly high reception scores to all neighboring sources. A smaller ℒγL_γ encourages the model to be selective about which neighbors contribute contextual information rather than reverting to indiscriminate neighbor aggregation. Propagation-mass regularization. The second regularizer controls the effective information mass transmitted along graph edges. Recall that (39) μu→it=aitbutγu→it, _u→ i^t=a_i^tb_u^t _u→ i^t, where aita_i^t indicates whether the target node is active, butb_u^t is the source forwarding budget and γu→it _u→ i^t is the source-reception strength. We regularize the average transmitted mass by (40) ℒμ=1T|ℰ|∑t=0T−1∑(u,i)∈ℰμu→it.L_μ= 1T|E| _t=0^T-1 _(u,i) _u→ i^t. Unlike ℒγL_γ, this term penalizes the realized information flow after accounting for target activity and source forwarding budget. It discourages excessive propagation even when individual reception scores remain moderate. Continuation regularization. The third regularizer controls the node-wise rollout length: (41) ℒa=1T||∑t=0T−1∑vi∈ait+1.L_a= 1T|V| _t=0^T-1 _v_i a_i^t+1. Since ait+1a_i^t+1 indicates whether node viv_i remains active after step t, minimizing ℒaL_a discourages unnecessarily long rollouts. This term prevents most nodes from remaining active until the maximum horizon while allowing nodes with positive predictive gain to continue collecting contextual information. Together, the three regularizers constrain node-level information flow from complementary perspectives. ℒγL_γ encourages selective source reception, ℒμL_μ limits the effective information mass transmitted along active paths and ℒaL_a promotes adaptive early stopping. In this way, the learned policy is discouraged from degenerating into uniform all-neighbor aggregation, excessive message transmission, or fixed full-horizon propagation. Appendix C Full Component Ablation Results Table 9 reports the complete ablation results on all ten node-level datasets. Removing source reception γ reduces the average accuracy from 0.4540 to 0.4388, showing that selective source acquisition helps suppress irrelevant neighboring evidence. Removing signal-channel selection ρ causes a larger average drop to 0.4200, with particularly clear degradation on Texas and Cornell. This confirms the importance of adapting the signal type to local topology. The largest performance decrease occurs when prediction–observation feedback is removed, reducing the average accuracy to 0.3646. The degradation is especially pronounced on Cora and Photo, indicating that feedback is central to assessing contextual reliability and correcting node states. Removing gain-aware stopping also lowers the average accuracy to 0.4282. Although the variant slightly improves results on Wisconsin and Chameleon, it degrades performance on most datasets, particularly PubMed, Computers and Photo.

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AgentGFM: A Graph Foundation Model with Node-Agent Information-Flow Control

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